Obama: "Yes, in fact, up at Camp David, we do skeet shooting all the time."

The president went on to say he has "a profound respect for the traditions of hunting that trace back in this country for generations."

Rep. Marsha Blackburn, R-Tenn., has stepped forward to say she has her doubts.

"If he is a skeet shooter why have we not heard of this, why have we not seen photos, why has he not referenced it at any point in time?" during the debate over gun laws, she asked Monday night on CNN.

Then Blackburn issued a challenge: "I think he should invite me to Camp David and I'll go skeet shooting with him and I bet I'll beat him."

At the White House on Monday, spokesman Jay Carney said he does not know how often the president has gone shooting at Camp David. As for whether there are pictures, Carney said he has not seen any. And, he added, when the president goes to Camp David, "he goes to spend time with his family and friends and relax, not to produce photographs."